►Fall 2016:
Accelerated Introduction to Computer Science
▼6 Assignments
►Doc  Diff
On this page:
1 Introduction
2 Assignment
3 Background
4 Code Template
5 Handing In
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1 Introduction

Consider the problem of comparing two text documents. Why might you want to do this? Perhaps you want to check for plagiarism, search for articles similar to a particular one you’re studying, or have uncovered a new manuscript and want to know whether it’s a legitimate Shakespeare or a fake. All these require being able to determine the similarity between documents. One way to model this similarity is as a distance metric, analogous to how we compute the distance between points in space. In this assignment we will define a document as list of strings, with each string representing a word. Here’s an example of a document:

[list: "The", "quick", "brown", "fox", "jumps"]

In order to compute the similarity between two documents, we associate each document with a mathematical vector, which here we will represent using a list of numbers. The indices of the vector correspond to words that are found in either document. The value at each index is how many times the corresponding word occurs in the document.

We assume that two words are the same if they have the same characters in the same order, ignoring upper- and lower-case (Pyret has functions to upper- or lower-case a string, and for sorting; you can look up these functions in the string and list libraries.)A smarter version of this program would ignore case for some words but not for ones that might also be proper nouns. Our distance measure is defined to be proportional to the dot product of these two document vectors:

\[distance(\vec{d_1}, \vec{d_2}) \propto \vec{d_1} \cdot \vec{d_2}\]

To obtain a formula, we normalize this dot-product. We will choose a simple method which is to divide by the squared magnitude of the larger vector:

\[distance(\vec{d_1}, \vec{d_2}) = \frac{\vec{d_1} \cdot \vec{d_2}}{max(\|\vec{d_1}\|^2,\|\vec{d_2}\|^2)}\]

where the magnitude of a vector \(\vec{x}\), denoted as \(\|\vec{x}\|\), is given by \(sqrt(\vec{x} \cdot \vec{x})\). Observe that this means every document will have a distance of 1 from itself, and any two documents that have no words in common will have distances of 0 from each other.

2 Assignment

Define a function

fun distance(doc1, doc): ... end

where doc1 and doc2 are lists of strings and distance returns a number. This function computes the distance between two non-empty documents, defined by the formula above.

Note that we are not asking you to consider efficiency of implementation.

3 Background

You may find this chapter useful in learning to program with lists in Pyret.

4 Code Template

Please use this.

5 Handing In

Captain Teach!

Your file must be named docdiff.arr.

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